The bicycle tires are provided with an air valve of the U.S. type or French type. The conventional bicycle air pump is not compatible with the air valves of both the U.S. type and the French type. However, the modem bicycle air pump comprises a nozzle which is provided with two connection heads engageable with the air valve of the U.S. type and the air valve of the French type. The selection of the connection heads is done manually, thereby discouraging the people to use the modem bicycle air pump as described above.